Question

A telephone tower casts a 50-foot shadow that makes a 48° angle with the ground. If Fiona wants to find the length of the cable that secures the tower to the ground, how should she set up the problem?

Option #1: cos48°=x50


Option #2: cos48°=50x


Option #3: cos50°=50x


(1 point)
Option #
is the correct setup.
Remaining Attempts : 3
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Answer 1

To find the length of the cable that secures the tower to the ground, we can use trigonometric relationships. In this scenario, we have a right triangle where:

- One leg is the height of the telephone tower (which we are interested in).
- The other leg is the length of the shadow cast (50 feet).
- The angle of elevation from the tip of the shadow to the top of the tower is 48°.

Since we want to find the length of the cable (hypotenuse), we can use the cosine function, which is defined as the ratio of the adjacent side (the shadow) to the hypotenuse (the cable). The correct trigonometric setup is:

\[
\cos(48°) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{50}{x}
\]

This can be rearranged to:

\[
x = \frac{50}{\cos(48°)}
\]

Thus, the correct option based on this setup is:

**Option #2: cos48° = 50/x**

So, you would select **Option #2** as the correct setup.